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Question

If P is a point (x,y) on the line y=āˆ’3x, such that P and the point (3,4) are on the opposite sides of the line 3xāˆ’4y=8, then

A
x>815
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B
x>85
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C
y<85
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D
y<815
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Solution

The correct options are
C x>815
D y<85
Let L=3x4y8=0 be the equation of line and P(x,y) and Q(3,4) are given points.
Then P and Q are on opposite side of the line iff L11L22<0
P is a point on the line y=3x.
i.e P=(x,3x)
L11L22=15x815<0
x>815
y=3x<85
Hence, options A and C.

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